How to project the lines of a basketball ball on an ancient greek head for 3D printing?
You could do it with a displace modifier. You just need a displacement map of your texture. I made mine with a normal map which was quickly done from a regular basketball texture so the result is not perfect. You really should use displacement map.
First you need to have enough resolution in your mesh. I had a head which had quite a lot of resolution but it still required 2x Subdivision Surface modifier. The Subdivision Surface modifier should be set to Simple not Catmull-Clark. In my example the deformation cannot be seen because there is a lot of geometry beforehand. Also give your mesh a Displace modifier. Next press New in the Displace modifier.

Press the Show texture in texture tab button in the Displace modifier.

Press Open and find your displacement map.

Set you Color Space to Non-Color.

Go back to Modifier Properties panel and in Displace Modifier set Coordinates to UV and decrease the Strength.

Remember to UV-unwrap your object so you get nice result. Next you can export the mesh from File -&gt; export -&gt; stl. Select Selection Only and Apply Modifiers.